Mr. A can do a piece of work in 24 days. After he had worked for 4 days, B joined him and together they completed the remaining work in 8 days. Then the numberof days in which B alone can complete the same work is

Let B alone can finish the work in x days.

A alone can finish the work in 24 days.

Hence A can finish the work in one day $$=\dfrac{1}{24}$$

So, A can finish the work in 4 days $$=\dfrac{4}{24}=\dfrac{1}{6}$$

The remaining work $$=\dfrac{5}{6}$$

A and B together can finish the work in one days $$\dfrac{1}{24}+\dfrac{1}{x}=\dfrac{5}{8\times 6}$$

$$\Rightarrow \dfrac{1}{x}=\dfrac{5}{48}-\dfrac{1}{24}=\dfrac{3}{48}$$

So, $$x=16$$days

Hence, B alone can finish the work in 16 days.